Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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BCCN Seminar

Friday, 22.07.2005 16 c.t.

Balanced Equivalence Relation, Quotient Network and Bursting in Coupled Cell System

by Prof. Dr. LieJune Shiau
from University of Houston, USA

Contact person: Marc Timme

Location

Seminarraum Haus 2, 4. Stock (Bunsenstr.)

Abstract

Abstract: Part I: The concepts of balanced equivalence relation and quotient network are introduced through illustrated examples. Some applications and importance of them are also pointed out. Part II: Periodic bursting has been studied, however, coupled cell network bursting has not. We focus on two identical cell systems and use the Z_2 symmetry present in such systems to illustrate interesting bursting phenomena. In particular, we show that Hopf/Hopf mode interactions can lead to bursting between in phase and out of phase periodic solutions and symmetry-breaking Takens-Bogdanov singularities can lead to bursting that randomly chooses between two (symmetrically related) limit cycles.

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